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The Versatility of Thermal Photons and Dileptons

The Versatility of Thermal Photons and Dileptons. Ralf Rapp Cyclotron Institute + Department of Phys & Astro Texas A&M University College Station, USA TPD Workshop BNL (Upton, NY), 05.-07.12.11. e + e -. γ. 1.) Introduction: Components of EM Probes HICs.

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The Versatility of Thermal Photons and Dileptons

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  1. The Versatility ofThermal Photons and Dileptons Ralf Rapp Cyclotron Institute + Department of Phys & Astro Texas A&M University College Station, USA TPD Workshop BNL (Upton, NY), 05.-07.12.11

  2. e+ e- γ 1.) Introduction:Components of EM Probes HICs • Thermal Emission Rate • micro-physics: • → Electro-Magnetic spectral function • Space-Time Evolution of Fireball • macro-physics (equation of state: e(P)) • → temperature + flow fields • Equation of State • - governed by micro-physics • (deg. of freedom, interactions) • - drives the macro-physics • - encodes deconfinement + chiral restoration

  3. Outline 2.) Transport Properties  EM Conductivity + Low-Energy Photons 3.) Spectral Properties  Vector Spectral Functions + the Fate of Resonances  Dilepton Invariant-Mass Spectra 4.) Chiral Restoration  Criteria: Axialvector, Lattice QCD, pert. QCD  QCD +Weinberg Sum Rules 5.) Fireball Properties  Lifetime, Temperature, Collectivity 6.) Conclusions

  4. 2.) Transport: Electric Conductivity • hadronic theories (T~150MeV): • - chiral pert. theory (pion gas): sem / T ~ 0.11 e2 • - hadronic many-body theory: sem / T ~ 0.09 e2 [Fernandez-Fraile+ Gomez-Nicola ’07] • lattice QCD (T ~ (1.5-3) Tc ): • sem /T ~ (0.26±0.02) e2 [Gupta ’04, Aarts et al ’07, Ding et al. ‘11] • soft-photon limit of • thermal emission rate • EM Susceptibility ( → charge fluctuations): • Q2 -Q 2 =χem = Πem(q0=0,q→0)

  5. Add pp→ppgBremsstrahlung [Liu+RR’06] 2.2 Soft Photons at SPS: WA98 Thermal Radiation + pQCD [Turbide,RR +Gale’04]

  6. Outline 2.) Transport Properties  EM Conductivity + Low-Energy Photons 3.) Spectral Properties  Vector Spectral Functions + the Fate of Resonances  Dilepton Invariant-Mass Spectra 4.) Chiral Restoration  Criteria: Axialvector, Lattice QCD, pert. QCD  QCD +Weinberg Sum Rules 5.) Fireball Properties  Lifetime, Temperature, Collectivity 6.) Conclusions

  7. 3.) EM Spectral Function I: Fate of Resonances Im Pem(M) in Vacuum Im Πem(M,q;mB,T) • Electromagn. spectral function • -√s ≤ 1 GeV: non-perturbative • -√s > 1.5 GeV: perturbative (“dual”) • Vector resonances “prototypes” • - representative for bulk hadrons: • neither Goldstone nor heavy flavor • Modifications of resonances • ↔ phase structure: • - hadron gas → Quark-Gluon Plasma • - realization of transition? e+e-→ hadrons √s = M

  8. 3.2 Phase Transition(s) in Lattice QCD - - ≈ qq / qq “Tcchiral”~150MeV “Tcconf” ~170MeV • different “transition” temperatures?! • smooth transitions! (smooth e+e- rate) • partial chiral restoration in “hadronic • phase” ?! (low-mass dileptons!) • leading-order hadron gas

  9. 3.3Vector Mesons in Hadronic Matter > rB /r0 0 0.1 0.7 2.6 > [Chanfray et al, Herrmann et al, Asakawa et al, RR et al, Koch et al, Klingl et al, Post et al, Eletsky et al, Harada et al …] Dr (M,q;mB ,T) = [M 2 - mr2 -Srpp -SrB -SrM ] -1 r-Propagator: B*,a1,K1... r Sp r SrB,rM= Selfenergies: Srpp= N,p,K… Sp Constraints:decays:B,M→ rN, rp, ... ; scattering:pN→rN, gA, … SPS RHIC

  10. 3.4 “Smoothness” of Dilepton Rates across “Tc” dRee /dM2 ~ ∫d3q f B(q0;T) Im Pem - • on-shell qq vs. pp annihil. • in transport code • smooth transition hadrons ↔ QGP?! • resonance melting + chiral mixing

  11. 3.5 Dilepton Rates vs. Exp.: NA60 “Spectrometer” • Evolve rates over fireball expansion: Thermal m+m- Emission Rate Acc.-correctedm+m- Excess Spectra In-In(158AGeV) [NA60 ‘09] Mmm [GeV] [van Hees+RR ’08] • invariant-mass spectrum directly • reflects thermal emission rate!

  12. 3.5.2 Sensitivity of NA60 to Spectral Function Emp. scatt. ampl. + T-r approximation Hadronic many-body Chiral virial expansion [CERN Courier Nov. 2009] • Significant differences in low-mass region • Overall slope T~150-200MeV (!)

  13. 3.5.3 Sensitivity to Spectral Function II • avg. Gr(T~150MeV)~350-400MeV • Gr (T~Tc) ≈ 600 MeV → mr • driven by baryons • Breit-Wigner shape insufficient: • ImSr ~ - q0 Gvac (1+ arB/r0) Mmm [GeV]

  14. 3.6 Low-Mass e+e- at RHIC: PHENIX vs. STAR • “large” enhancement not accounted • for by theory • QGP radiation not an option… • (very) low-mass region • overpredicted?! (SPS?!)

  15. Outline 2.) Transport Properties  EM Conductivity + Low-Energy Photons 3.) Spectral Properties  Vector Spectral Functions + the Fate of Resonances  Dilepton Invariant-Mass Spectra 4.) Chiral Restoration  Criteria: Axialvector, Lattice QCD, pert. QCD  QCD +Weinberg Sum Rules 5.) Fireball Properties  Lifetime, Temperature, Collectivity 6.) Conclusions

  16. 4.) Criteria for Chiral Restoration • Vector (r) – Axialvector (a1) degenerate [Weinberg ’67, Das et al ’67] pQCD • QCD sum rules: • medium modifications ↔ vanishing of condensates • Agreement with thermal lattice-QCD • Approach to perturbative rate (QGP)

  17. p Sp Sp Sp r Sr Sr Sr 4.1 Axialvector in Medium: Dynamical a1(1260) p a1 resonance + + . . . = Vacuum: r In Medium: + + . . . [Cabrera,Jido, Roca+RR ’09] • in-medium p + r propagators • broadening of p-r scatt. Amplitude • pion decay constant in medium:

  18. 0.2% 1% 4.2 QCD Sum Rules: r(770) in Nuclear Matter [Shifman,Vainshtein,+Zakharov ’79] • dispersion relation: [Hatsuda+Lee’91, Asakawa+Ko ’92, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05] • rhs:hadronic model (s>0): • lhs:OPE (spacelike Q2): nonpert. Wilson coeffs. (condensates) • ~50% reduced in nuclear matter ◊ ← vacuum

  19. 4.3 Hadronic - Perturbative QGP - Lattice QCD dRee /dM2 ~ ∫d3q f B(q0;T) Im Pem • Hadronic, pert. + lattice QCD • tend to “degenerate” toward~Tc • Quark-Hadron Duality at all M?! • ( degenerate axialvector SF!) dRee/d4q 1.4Tc (quenched) q=0 - [qq→ee] [HTL] [Ding et al ’10] [RR,Wambach et al ’99]

  20. 4.3.2 Euclidean Correlators: Lattice vs. Hadronic • Euclidean Correlation fct. Lattice (quenched) [Ding et al ‘10] Hadronic Many-Body [RR ‘02] • “Parton-Hadron Duality” of lattice and in-medium hadronic?!

  21. 4.3.3 Back to Spectral Function -Im Pem /(C T q0) • suggests approach to chiral restoration + deconfinement

  22. Outline 2.) Transport Properties  EM Conductivity + Low-Energy Photons 3.) Spectral Properties  Vector Spectral Functions + the Fate of Resonances  Dilepton Invariant-Mass Spectra 4.) Chiral Restoration  Criteria: Axialvector, Lattice QCD, pert. QCD  QCD +Weinberg Sum Rules 5.) Fireball Properties  Lifetime, Temperature, Collectivity 6.) Conclusions

  23. 5.1 Low-Mass Dileptons: Chronometer In-In Nch>30 • first “explicit” measurement of interacting-fireball lifetime: • tFB≈ (6.5±1) fm/c • search for critical slowing down!

  24. 5.2 Intermediate-Mass Dileptons: Thermometer • use invariant continuum radiation (M>1GeV): no blue shift, Tslope = T ! Thermometer • independent of partition HG vs QGP (dilepton rate continuous/dual) • initial temperature Ti ~ 190-220 MeV at CERN-SPS

  25. 5.3 Dimuon pt-Spectra and Slopes: Barometer Effective Slopes Teff • theo. slopes originally too soft • increase fireball acceleration, • e.g. a┴ = 0.085/fm → 0.1/fm • insensitive to Tc=160-190MeV

  26. 5.4 Direct Photons at RHIC Spectra Elliptic Flow ← excess radiation • Teffexcess = (220±25) MeV • QGP radiation? • radial flow? • v2g,dir as large as that of pions!? • underpredcited by QGP-dominated • emission [Holopainen et al ’11,…]

  27. 5.4.1 Revisit Ingredients Emission Rates Fireball Evolution • multi-strange hadrons at “Tc” • v2bulkfully built up at hadronization • chemical potentials for p, K, … • Hadron - QGP continuity! [Turbide et al ’04] [van Hees et al ’11]

  28. 5.4.2 Thermal Photon Spectra + v2: PHENIX thermal + prim. g • both spectral slope and v2 point at • blue-shifted hadronic source… • to be tested in full hydro [van Hees,Gale+RR ’11]

  29. 6.) Conclusions:Potential of Thermal EM Radiation at RHIC • Transport: conductivity, susceptibility (→ diffusion, h/s) • Spectrometer: “prototype” in-med. spectral function, • hadron-to-quark transition • Chiral Restoration: Weinberg + QCD sum rules, • lattice QCD (mB~0!) + perturbative limit • Thermometer: int.-mass dileptons (heavy-flavor subtracted) • Chronometer: search for anomalous fireball lifetimes • Barometer: pt spectra (M=0-2GeV) • Quality control: rates (constraints, continuity), medium evolution, • consistency with SPS, … • Needed: NA60-quality data • RHIC premiere facility for soft EM probes of transition region

  30. 2.3.2 NA60 Mass Spectra: pt Dependence Mmm [GeV] • more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout r , …

  31. 4.1.2 Mass-Temperature Emission Correlation • generic space-time argument: •  • Tmax ≈ M / 5.5 • (forImPem =const) • thermal photons: • Tmax≈ (q0/5) * (T/Teff)2 • → reduced by flow blue-shift! • Teff ~ T * √(1+b)/(1-b)

  32. 4.7.2 Light Vector Mesons at RHIC + LHC • baryon effects important even at rB,tot= 0 : • sensitive to rBtot= rB + rB (r-N and r-N interactions identical) • w also melts, f more robust ↔ OZI - -

  33. = = 5.3 Intermediate Mass Emission: “Chiral Mixing” [Dey, Eletsky +Ioffe ’90] • low-energy pion interactions fixed by chiral symmetry 0 0 0 0 • mixing parameter • degeneracy with perturbative • spectral fct. down to M~1GeV • physical processes at M≥ 1GeV: • pa1→ e+e- etc. (“4p annihilation”)

  34. 3.2 Dimuon pt-Spectra and Slopes: Barometer pions: Tch=160MeV a┴ =0.1/fm pions: Tch=175MeV a┴ =0.085/fm • modify fireball evolution: • e.g. a┴ = 0.085/fm → 0.1/fm • both large and small Tccompatible • with excess dilepton slopes

  35. 2.3.2 Acceptance-Corrected NA60 Spectra Mmm [GeV] Mmm [GeV] • more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout r , …

  36. 4.4.3 Origin of the Low-Mass Excess in PHENIX? • QGP radiation insufficient: • space-time , lattice QGP rate + • resum. pert. rates too small • must be of long-lived hadronic origin • Disoriented Chiral Condensate (DCC)? • Lumps of self-bound pion liquid? • Challenge: consistency with hadronic data, NA60 spectra! [Bjorken et al ’93, Rajagopal+Wilczek ’93] - “baked Alaska” ↔ small T - rapid quench+large domains ↔ central A-A - ptherm + pDCC → e+ e- ↔ M~0.3GeV, small pt [Z.Huang+X.N.Wang ’96 Kluger,Koch,Randrup ‘98]

  37. 2.2 EM Probes at SPS • all calculated with the same e.m. spectral function! • thermal source: Ti≈210MeV, HG-dominated, r-meson melting!

  38. 2.3.3 Spectrometer III: Before Acceptance Correction emp. ampl. + “hard” fireball hadr. many-body + fireball schem. broad./drop. + HSD transport chiral virial + hydro • Discrimination power much reduced • can compensate spectral “deficit” by larger flow: lift pairs into acceptance

  39. 4.2 Improved Low-Mass QGP Emission • LO pQCD spectral function: rV(q0,q) = 6∕9 3M2/2p [1+QHTL(q0)] • 3-momentum augmented lattice-QCD rate (finite g rate)

  40. 4.4.1 Variations in QGP Radiation • improvements in QGP rate insufficient

  41. 4.4.2 Variations in Fireball Properties • variations in space-time evolution only • significant in (late) hadronic phase

  42. 4.1 Nuclear Photoproduction: rMeson in Cold Matter g + A → e+e- X • extracted • “in-med” r-width • Gr≈ 220 MeV e+ e- Eg≈1.5-3 GeV g r [CLAS+GiBUU ‘08] • Microscopic Approach: + in-med. r spectral fct. product. amplitude full calculation fix density 0.4r0 Fe-Ti r g N [Riek et al ’08, ‘10] M[GeV] • r-broadening reduced at high 3-momentum; need low momentum cut!

  43. 1.2 Intro-II:EoS and Particle Content • Hadron Resonance Gas until close to Tc • - but far from non-interacting: • short-lived resonances R: • a + b → R → a + b,tR ≤ 1 fm/c • Parton Quasi-Particles shortly above Tc • - but large interaction measure I(T) = e -3P  both “phases” strongly coupled (hydro!): - large interaction rates → large collisional widths - resonance broadening → melting → quarks - broad parton quasi-particles - “Feshbach” resonances around Tc (coalescence!)

  44. 2.3.6 Hydrodynamics vs. Fireball Expansion • very good agreement • between original • hydro [Dusling/Zahed] • and fireball [Hees/Rapp]

  45. e+ e- γ 2.1 Thermal Electromagnetic Emission EM Current-Current Correlation Function: Thermal Dilepton and Photon Production Rates: Im Πem(M,q) Im Πem(q0=q) r-meson dominated Low Mass: ImPem~ [ImDr + ImDw /10 + ImDf /5]

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